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A Golden Rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1:1.618. It's considered aesthetically pleasing and appears frequently in art, architecture, and nature.
The calculator uses the formula:
Where:
Explanation: This formula calculates the shorter side (breadth) of a golden rectangle when the total perimeter is known, using the mathematical properties of the golden ratio.
Details: The golden rectangle has been used in art and architecture for centuries due to its visually pleasing proportions. Understanding its mathematical properties helps in design, aesthetics, and various mathematical applications.
Tips: Enter the perimeter value in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is the golden ratio?
A: The golden ratio (φ) is an irrational number approximately equal to 1.618, often found in nature, art, and architecture as a proportion considered aesthetically pleasing.
Q2: How is the golden rectangle different from a regular rectangle?
A: In a golden rectangle, the ratio of the longer side to the shorter side equals the golden ratio (φ ≈ 1.618:1), creating a specific proportional relationship.
Q3: Where are golden rectangles commonly found?
A: Golden rectangles appear in famous artworks (like the Mona Lisa), architectural designs (Parthenon), and even in the proportions of credit cards and photographs.
Q4: Can I calculate the length if I know the breadth?
A: Yes, the length of a golden rectangle is simply the breadth multiplied by the golden ratio (φ ≈ 1.618).
Q5: What's the relationship between perimeter and the sides?
A: For any rectangle, perimeter = 2 × (length + breadth). For a golden rectangle, this becomes P = 2 × (b × φ + b) = 2b(1 + φ).